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A134028 Reversal of n in balanced ternary representation. 14

%I #35 Mar 17 2021 08:02:55

%S 0,1,-2,1,4,-11,-2,7,-8,1,10,-5,4,13,-38,-11,16,-29,-2,25,-20,7,34,

%T -35,-8,19,-26,1,28,-17,10,37,-32,-5,22,-23,4,31,-14,13,40,-119,-38,

%U 43,-92,-11,70,-65,16,97,-110,-29,52,-83,-2,79,-56,25,106,-101,-20,61,-74,7,88,-47,34,115,-116,-35,46,-89,-8,73,-62,19,100

%N Reversal of n in balanced ternary representation.

%C As the graph demonstrates, the sequence makes large negative steps at terms (3^i+1)/2. These steps divide the graph into conspicuous blocks. - _N. J. A. Sloane_, Jul 03 2016

%D D. E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, Vol 2, pp 173-175.

%H Reinhard Zumkeller, <a href="/A134028/b134028.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Reversal.html">Reversal</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Balanced_ternary">Balanced Ternary</a>

%F a(A134027(n)) = A134027(n);

%F A134021(ABS(a(n))) <= A134021(n).

%e 20 = 1*3^3 - 1*3^2 + 1*3^1 - 1*3^0 == '+-+-'

%e => a(20) = -1*3^3 + 1*3^2 - 1*3^1 + 1*3^0 = -20;

%e 21 = 1*3^3 - 1*3^2 + 1*3^1 + 0*3^0 == '+-+0'

%e => a(21) = 0*3^3 + 1*3^2 - 1*3^1 + 1*3^0 = 7;

%e 22 = 1*3^3 - 1*3^2 + 1*3^1 + 1*3^0 == '+-++'

%e => a(22) = 1*3^3 + 1*3^2 - 1*3^1 + 1*3^0 = 34;

%e 23 = 1*3^3 + 0*3^2 - 1*3^1 - 1*3^0 == '+0--'

%e => a(23) = -1*3^3 - 1*3^2 + 0*3^1 + 1*3^0 = -35;

%e 24 = 1*3^3 + 0*3^2 - 1*3^1 + 0*3^0 == '+0-0'

%e => a(24) = 0*3^3 - 1*3^2 + 0*3^1 + 1*3^0 = -8;

%e 25 = 1*3^3 + 0*3^2 - 1*3^1 + 1*3^0 == '+0-+'

%e => a(25) = 1*3^3 - 1*3^2 + 0*3^1 + 1*3^0 = 19.

%o (Python)

%o def a(n):

%o if n==0: return 0

%o s=[]

%o x=0

%o while n>0:

%o x=n%3

%o n=n//3

%o if x==2:

%o x=-1

%o n+=1

%o s.append(x)

%o l=s[::-1]

%o return sum(l[i]*3**i for i in range(len(l)))

%o print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 10 2017

%Y Cf. A117966 (balanced ternary representation), A030102, A134021, A274107.

%Y A134027 gives the numbers whose balanced ternary representation is palindromic.

%K sign,look,base

%O 0,3

%A _Reinhard Zumkeller_, Oct 19 2007

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)